5/7p-2/6p+12=6

Solution for 5/7p-2/6p+12=6 equation:

5/7p-2/6p+12=6

We move all terms to the left:

5/7p-2/6p+12-(6)=0


Domain of the equation: 7p!=0

p!=0/7

p!=0

p∈R



Domain of the equation: 6p!=0

p!=0/6

p!=0

p∈R


We add all the numbers together, and all the variables

5/7p-2/6p+6=0

We calculate fractions


30p/42p^2+(-14p)/42p^2+6=0

We multiply all the terms by the denominator


30p+(-14p)+6*42p^2=0

Wy multiply elements

252p^2+30p+(-14p)=0

We get rid of parentheses

252p^2+30p-14p=0

We add all the numbers together, and all the variables

252p^2+16p=0

a = 252; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·252·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*252}=\frac{-32}{504}
=-4/63
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*252}=\frac{0}{504}
=0
$